Title is no doubt crafted to get ahead of the usual online backlash, but here’s the actual announcement:
> We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory.
1. Local smoothing and the Kakeya conjecture
2. The Exponential Time Hypothesis is false
3. Existence of quantum chromodynamics and completions of the Standard Model
this is the first time one of the big labs has published anything related to my field. and i'm actually pretty excited? im more on the applications side of QFD than the theory side of things, but gosh i actually cant wait for the results to be released to see if i can use it for anything! i kinda hope more results come out, in more ways relevant to what i do, its so cool to see any sort of progress! wow!
ETH is false! This is one of the big long-standing hypotheses that I actually remember from university, and afaik, it was reasonable to assume it would be true; reasonable enough for a lot of papers and results to assume this for bounds or hardness proofs of common problems in parameterized complexity, anyways.
Also glad to see that one of the authors of the paper stating it is also in the loop here.
I understand that the Exponential Time Hypothesis being false doesn't necessarily mean P=NP, but for people who are a lot more knowledgeable about complexity theory, does this update your priors significantly in the direction of P=NP?
> Our models produced a natural language proof for Yang–Mills existence on September 9th, 2026, and then subsequently produced a proof for QCD on September 18th, 2026. Given the length and complexity of the work, we postponed release until the Lean formalization completed. We finished our formalization of Yang–Mills’ existence on October 16th, 2026, which led us to develop the collaboration described here
Lots of progress recently in formally verifiable domains. Really curious if this is a product of the machine learning folks behind most large language models being much more likely to have a background in math, physics, etc. Or if it is that large language models have some fundamental limitations in the more "scruffy" sciences like biology.
My guess is that in formally verifiable domains you can use RL-esque processes to get lots of good high-quality training data with reward signals (does it verify?), but the same does not apply to "scruffier" work. I would also imagine that the data volume of high-quality scientific work in "scruffy" domains is too low for the large language models to have a good manifold for "high-quality biology research". Would love to be proven wrong if anyone knows of anyone doing great scientific work with large language models in non-verifiable domains though.
Regarding Yang-Mills, as of a few weeks ago there has been some expectation that this (specifically completing Balaban's program for the existence part without the mass gap) could happen, though from the Anthropic side: https://nitter.meowing.monster/ElliotGlazer/status/211115394...
(Elliot Glazer seems in general to be a pretty good source to follow, however he does that...)
Well, this is certainly different, can't say they ignored the criticism. Wonder if this is a monkey paw curls moment; if the findings continue to accelerate, most of it just isn't public now.
> In our view, these manuscripts are best understood as a form of raw research data. To convert this raw research data into scientific understanding, in this release we are experimenting with a new approach
Mathematics and computer science are turning into an empirical science
I am not sure if I side with Tao on this, or 3B1B. It's already causing quite a kerfuffle (to say the least) in the academic communities. This is the new norm now.
I wonder why the physicists are the only group to not want the full information released upfront? As a casual fan of physics[0] it seems like their completion of the standard model is possibly the biggest deal of all these breakthroughs, am I wrong?
I wonder how much compute they are throwing at problems in ML like continual learning and sample efficiency. Also how successful they are with these. Results like in the post make me hopeful we'll see some type of so singularity soon
> In our view, these manuscripts are best understood as a form of raw research data.
Much better!
> For the computer science collaboration, the group has decided to make the natural language proof and Lean formalization public immediately, and we are publishing them directly to our GitHub repository. For the physics collaboration, the group has decided to hold off on releasing the AI-produced artifacts and instead work on writing it up themselves.
> All of these approaches involve tradeoffs. On the one hand, the collaborations empower experts to foster unpacking the results and contextualizing them in the broader academic community. On the other hand, choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information. We welcome feedback on how to broaden participation and make this process more useful.
Very good!
I was highly critical of their approach with the earlier mathematical publications, but this is much improved.
Most importantly, they aren't releasing slop papers that would never have been published in any self-respecting journal or made it past a deep round of peer review questioning.
> We are committed to ensuring funding for researchers to independently examine, explain, and build on the results above.
> We continue to invite feedback on the best way to disclose results and engage with scientists to accelerate discovery.
Well done!
Now you need to actually LISTEN to the community and the feedback, so you aren't done yet, but this is a much better start than last time. Keep it up!
> We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory.
1. Local smoothing and the Kakeya conjecture
2. The Exponential Time Hypothesis is false
3. Existence of quantum chromodynamics and completions of the Standard Model
Also glad to see that one of the authors of the paper stating it is also in the loop here.
2026 is weird.
absolutely insane
My guess is that in formally verifiable domains you can use RL-esque processes to get lots of good high-quality training data with reward signals (does it verify?), but the same does not apply to "scruffier" work. I would also imagine that the data volume of high-quality scientific work in "scruffy" domains is too low for the large language models to have a good manifold for "high-quality biology research". Would love to be proven wrong if anyone knows of anyone doing great scientific work with large language models in non-verifiable domains though.
> The Exponential Time Hypothesis is false
(Elliot Glazer seems in general to be a pretty good source to follow, however he does that...)
Mathematics and computer science are turning into an empirical science
Let's throw in more of that stuff, so they wouldn't look at the financials.
[0]: PBS space time watcher
Much better!
> For the computer science collaboration, the group has decided to make the natural language proof and Lean formalization public immediately, and we are publishing them directly to our GitHub repository. For the physics collaboration, the group has decided to hold off on releasing the AI-produced artifacts and instead work on writing it up themselves.
> All of these approaches involve tradeoffs. On the one hand, the collaborations empower experts to foster unpacking the results and contextualizing them in the broader academic community. On the other hand, choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information. We welcome feedback on how to broaden participation and make this process more useful.
Very good!
I was highly critical of their approach with the earlier mathematical publications, but this is much improved.
Most importantly, they aren't releasing slop papers that would never have been published in any self-respecting journal or made it past a deep round of peer review questioning.
> We are committed to ensuring funding for researchers to independently examine, explain, and build on the results above.
> We continue to invite feedback on the best way to disclose results and engage with scientists to accelerate discovery.
Well done!
Now you need to actually LISTEN to the community and the feedback, so you aren't done yet, but this is a much better start than last time. Keep it up!